There are two things that determine how fast a refrigerator gets cold.
Now the BTU of heat removed can be Rate of input refrigeration BTU/time minus insulation heat loss BTU/time. If the number is positive it will cool down and the mor positive it is, the faster it will cool. Presuming the system has a thermostat it will shut off the refrigeration and not overcool.
But the speed depends on those factors I mentioned.